The random variable itself is the process dictating how the observation comes about.
Conventionally, to avoid confusion, upper case letters denote random variables; the corresponding lower case letters denote their realizations.
Elements of the sample space can be thought of as all the different possibilities that could happen; while a realization (an element of the state space) can be thought of as the value X attains when one of the possibilities did happen.
Probability is a mapping that assigns numbers between zero and one to certain subsets of the sample space, namely the measurable subsets, known here as events.
Subsets of the sample space that contain only one element are called elementary events.